J. Phys. Chem. B 2006, 110, 6279-6292
6279
Development of Many-Body Polarizable Force Fields for Li-Battery Components: 1. Ether, Alkane, and Carbonate-Based Solvents Oleg Borodin*,† and Grant D. Smith†,‡ Department of Materials Science & Engineering, 122 South Central Campus DriVe, Room 304, UniVersity of Utah, Salt Lake City, Utah 84112, and Department of Chemical Engineering, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed: September 8, 2005; In Final Form: January 3, 2006
Classical many-body polarizable force fields were developed for n-alkanes, perflouroalkanes, polyethers, ketones, and linear and cyclic carbonates on the basis of quantum chemistry dimer energies of model compounds and empirical thermodynamic liquid-state properties. The dependence of the electron correlation contribution to the dimer binding energy on basis-set size and level of theory was investigated as a function of molecular separation for a number of alkane, ether, and ketone dimers. Molecular dynamics (MD) simulations of the force fields accurately predicted structural, dynamic, and transport properties of liquids and unentangled polymer melts. On average, gas-phase dimer binding energies predicted with the force field were between those from MP2/aug-cc-pvDz and MP2/aug-cc-pvTz quantum chemistry calculations.
I. Introduction Numerous force fields have been developed for simulations of liquids, proteins, amino acids, and polymers over the last 25 years. These force fields can be divided, in general, into three categories: (a) force fields parametrized on the basis of a broad training set of molecules such as small organic molecules, peptides, or amino acids including AMBER,12-3 COMPASS,4,5 OPLS-AA,6 and CHARMM,7 and a few many-body polarizable force fields;8-10 (b) generic potentials such as DREIDING11 and UNIVERSAL12 that are not parametrized to reproduce properties of any particular set of molecules; and (c) specialized force fields carefully parametrized to reproduce properties of a specific compound such as water,13,14,15 specific polymers,16 polymer aqueous solutions,17 and polymer electrolytes,18,19 etc. In choosing a force field for a specific application, care must be taken to ensure that all dominant interactions (electrostatics, polarization, hydrogen bonding, etc) are adequately included, the force field parametrization is performed on compounds of interest or closely related compounds or the force field transferability has been carefully studied, and, finally, the properties of interest were either included in the parametrization of the force field of choice or were shown to be adequately predicted by the force field for similar compounds. For example, a description of thermodynamic properties does not necessarily translate into an adequate prediction of transport properties for liquids and oligomers. Specifically, the OPLS-AA force field parametrized against liquid density, heat of vaporization, and ab initio quantum chemistry-based conformational energetics predicts viscosity of n-octane to be 45-100% higher than experiments.20 A united atom force field designed for the accurate prediction of vapor-liquid equilibrium of perfluoroalkanes predicts a significantly lower (by a factor of 2-5) viscosity of them.21 Some quantum chemistry-based force fields * To whom correspondence should be addressed. E-mail: borodin@ eng.utah.edu. † Department of Materials Science & Engineering. ‡ Department of Chemical Engineering.
fail to accurately predict thermodynamic properties, e.g., the Merk MMFF94 force field parametrized on the basis of scaled low-level quantum chemistry data systematically predicts heats of sublimations 30-40% too low22 for a number of alkane and nonalkane compounds and does not predict a stable n-butane liquid at -0.5 °C.23 Our goal is to obtain a force field that reliably predicts thermodynamic, structural, and transport properties of electrolytes composed of Li-salts dissolved in nonaqueous liquids, polymer melts, and their combination (gel or plasticized electrolytes) that are aimed, but not limited, to Li-metal and Li-ion battery applications. A key decision we need to make at the beginning of force field development is whether to include solvent polarization explicitly in the force field, through inclusion of dipole polarizability terms, or use computationally inexpensive fluctuating charge or an effective two-body potential. Experience with employing effective two-body force fields for simulating liquids and their interactions with large monovalent cations, such as a K+ cation,24 indicates that effective twobody potentials such as OPLS-AA usually adequately predict thermodynamic, structural, and often transport properties of pure liquids and dissociated electrolytes. However, significant deviations of predicted properties are sometimes reported even for pure polar liquids when two-body force fields are utilized. For example, Tasaki25 reported in a recent simulation study of propylene carbonate (PC) and dimethyl carbonate (DMC) liquids employing a proprietary COMPASS force field room-temperature densities of 1.03 ( 0.01 and 1.03 ( 0.00 g/cm3 for PC and DMC, respectively, which are 13 and 7% lower than experimental densities of PC and DMC. Li+ is a much smaller cation than the K+ cation. This allows + Li to closely approach a solvent and/or an anion and significantly polarize them. Our previous quantum chemistry studies26,27 of Li+/anion and Li+/1,2-dimethoxyethane (DME) interactions indicated that polarization of anions (PF6-, BF4-) and DME by Li+ accounts for approximately one-third of the binding energy, thus stressing the need for an accurate representation of polarization effects in the Li+/anion/solvent force
10.1021/jp055079e CCC: $33.50 © 2006 American Chemical Society Published on Web 03/04/2006
6280 J. Phys. Chem. B, Vol. 110, No. 12, 2006 field. The importance of the inclusion of water polarization by a Li+ was also evident from Li+/water simulation studies,28 where two-body force fields parametrized based upon Li+‚‚‚ H2O dimer energies dramatically overestimated Li+ energy of hydration and yielded an incorrect coordination number. Although the inclusion of many-body polarizable terms in the force field is the most rigorous approach to incorporating these effects, numerous studies reported using two-body force fields that effectively take solvent polarization into account.18,19,26-28 Parametrization of such effective two-body force fields is based either on energies for removal of one solvent molecule from a completed Li+ first-solvation shell obtained from quantum chemistry calculations,28 as was done for Li+/water, or by replacing many-body terms with effective two-body polarizable terms in a force field to reproduce lithium coordination from simulations with many-body potentials.18 Such approaches often accurately reproduce a number of solvent molecules coordinating Li+ but were found less reliable than many-body force fields in predicting solvation energies and, in our experience, predicted significantly longer Li+/solvent residence times than simulations employing many-body polarizable force fields.18 Previous Polarizable Force Fields. Recent work on the development of robust quantum chemistry-based polarizable force fields for organic molecules8-10,18,19 and ion/water29 interactions indicated high accuracy of simulation predictions of structural and thermodynamic properties. These force fields are typically based on heat of vaporization, liquid density, and gas-phase dimer binding energies obtained from ab initio quantum chemistry calculations8-10,18,19 or symmetry-adapted perturbation theory.30 Kaminsky et al.10 determined polarizabilities and most nonbonded parameters for organic liquids on the basis of quantum-chemistry data except for the dispersion parameters, which where determined by fitting heats of vaporization and liquid density. Molecular dynamics (MD) simulations with the resulting force field predicted densities within 5% and heats of vaporizations within 0.5 kcal/mol for a series of small molecules. This approach is similar to our methodology previously used in the development of the many-body polarizable potential for PEO/LiBF4,19 in which atomic polarizabilities were fitted to reproduce a polarization response due to the 1e test charge and nonbonded parameters were reoptimized to fit liquid density, heat of vaporization, and ether dimer binding energies determined using Møller-Plesset second-order perturbation theory (MP2) with the complete basis set extrapolation. In this work, we extend our previous approach19 to the development of many-body polarizable force fields for linear oligoethers with the structure CH3-((CH2)n-O)m-O-CH3 n ) 1-3 (POM, PEO, and PTMO, respectively),31 combbranched polyepoxide ethers (PEPE), PPO, EC, PC, DMC, and GBL (see Table 1 for a list of abbreviations) on the basis of gas-phase dimer energies, liquid densities, heats of vaporization, and alkane self-diffusion coefficients. We will use an atomic dipole polarizable model because it describes the electrostatic response better than the fluctuating charge model.32,33 MD simulations employing the developed force field are discussed with the emphasis on the ability to reliably predict static structure factors, dielectric loss, 13C NMR spin-lattice relaxation times, and incoherent intermediate structure factors. In the follow-up paper,34 we report the development of the lithium trifluoromethanesulfonylimide (LiTFSI, or LiCF3SO2NSO2CF3) force field and MD simulations of a number of nonaqueous liquid electrolytes and polymer electrolytes doped with LiTFSI, focusing on the prediction of ion aggregation and transport properties.
Borodin and Smith TABLE 1: List of Abbreviated Molecular Names Used in This Paper DME - 1,2-dimethoxyethane CH3OCH2CH2OCH3 DMM - dimethoxymethane CH3OCH2OCH3 1,2-DMP - 1,2 dimethoxypropane CH3OCH(CH3)CH2OCH3 1,3-DMP - 1,3 dimethoxypropane CH3OCH2CH2CH2OCH3 OM3DMM - CH3OCH2(OCH2)3OCH3 EC - ethylene carbonate PC - propylene carbonate DMC - dimethyl carbonate GBL - γ-Butyrolactone DMA - dimethylamine PEO - poly(ethylene oxide) POM - poly(oxymethylene) PTMO - poly(trimethylene oxide) PPO - poly(propylene oxide) PEPE - poly(epoxide ether)
II. Force Field Development Methodology A. Force Field Functional Form. In our classical force field the total potential energy of the ensemble of atoms, represented by the coordinate vector r, is denoted as Utot(r). The latter is represented as a sum of nonbonded interactions UNB(rij) as well as energy contributions due to bonds UBOND(rij) having bond length rij, bends UBEND(θijk) having bending angle θijk and dihedrals UTORS(φijkl) with dihedral angle φijkl and is given by eq 1
Utot(r) )
UNB(rij) + ∑ UBOND(rij) + ∑ UBEND(θijk) + ∑ iβ
〉)
(a12)
where
LRβ(t) )
∫0t PRβ(t′)dt′
kB is the Boltzmann constant, T is temperature, t is time, PRβ is the symmeterized stress sensor, and V is the volume of the simulation box. Supporting Information Available: A summary of conformational energetics from quantum chemistry calculations and developed force field is included in Supporting Information A. Developed force field parameters for solvents and their interaction with LiTFSI are listed in Supporting Information B. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Cornell, W. D. et al. J. Am. Chem. Soc. 1995, 117, 5179. (2) Wang, J.; Ceiplak, P.; Kollman, P. J. Comput. Chem. 2000, 21, 1049. (3) Cieplak, P.; Caldwell, J.; Kollman, P. J. Comput. Chem. 2001, 22, 1048. (4) Sun, H. J. Phys. Chem. B 1998, 102, 7338. (5) Rigby, D.; Sun, H.; Eichinger, B. E. Polym. Int. 1997, 44, 311. (6) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. (7) MacKerell, A. D. et al. J. Phys. Chem. B 1998, 102, 3586.
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